The term b-tree refers to a way of organizing database information so that you can quickly search through it to find exactly what you're looking for. B-tree is a way of organizing database keys so you can quickly search them on disk.
A database contains collections of related information, similar to file cards. Each record contains several fields, such as name, address, date of birth, etc. We want to find something based on one of those pieces of information. We could search sequentially through the whole file, but imagine if you had to search through the entire database of California social security numbers one by one. A b-tree allows you to search efficiently for specific names or numbers even as you are adding or deleting from the database. It dynamically grows and shrinks and maintains an up-to-date index stored as a tree, hence the name. (The letter "b" is to differentiate from other types of previously existing trees.)